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Stochastic networks / Frank Kelly, Elena Yudovina.

Communication networks underpin our modern world, and provide fascinating and challenging examples of large-scale stochastic systems. Randomness arises in communication systems at many levels: for example, the initiation and termination times of calls in a telephone network, or the statistical struc...

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Kelly, Frank, 1950-
Other Authors: Yudovina, Elena
Format: eBook
Language:English
Published: Cambridge, U.K. : Cambridge University Press, 2014.
Series:Institute of Mathematical Statistics textbooks.
Subjects:
Stochastic models.
Telecommunication > Mathematical models.
Stochastic models
Telecommunication > Mathematical models
Table of Contents:
  • Machine generated contents note: Queueing and loss networks
  • Decentralized optimization
  • Random access networks
  • Broadband networks
  • Internet modelling
  • Part I
  • 1. Markov chains
  • 1.1. Definitions and notation
  • 1.2. Time reversal
  • 1.3. Erlang's formula
  • 1.4. Further reading
  • 2. Queueing networks
  • 2.1. An M/M/1 queue
  • 2.2.A series of M/M//1 queues
  • 2.3. Closed migration processes
  • 2.4. Open migration processes
  • 2.5. Little's law
  • 2.6. Linear migration processes
  • 2.7. Generalizations
  • 2.8. Further reading
  • 3. Loss networks
  • 3.1.Network model
  • 3.2. Approximation procedure
  • 3.3. Truncating reversible processes
  • 3.4. Maximum probability
  • 3.5.A central limit theorem
  • 3.6. Erlang fixed point
  • 3.7. Diverse routing
  • 3.8. Further reading
  • Part II
  • 4. Decentralized optimization
  • 4.1. An electrical network
  • 4.2. Road traffic models
  • 4.3. Optimization of queueing and loss networks
  • 4.4. Further reading
  • 5. Random access networks.
  • Note continued: 5.1. The ALOHA protocol
  • 5.2. Estimating backlog
  • 5.3. Acknowledgement-based schemes
  • 5.4. Distributed random access
  • 5.5. Further reading
  • 6. Effective bandwidth
  • 6.1. Chernoff bound and Cramer's theorem
  • 6.2. Effective bandwidth
  • 6.3. Large deviations for a queue with many sources
  • 6.4. Further reading
  • Part III
  • 7. Internet congestion control
  • 7.1. Control of elastic network flows
  • 7.2. Notions of fairness
  • 7.3.A primal algorithm
  • 7.4. Modelling TCP
  • 7.5. What is being optimized?
  • 7.6.A dual algorithm
  • 7.7. Time delays
  • 7.8. Modelling a switch
  • 7.9. Further reading
  • 8. Flow level Internet models
  • 8.1. Evolution of flows
  • 8.2.[alpha]-fair rate allocations
  • 8.3. Stability of [alpha]-fair rate allocations
  • 8.4. What can go wrong?
  • 8.5. Linear network with proportional fairness
  • 8.6. Further reading.

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